Serial killer Levi Bellfield has confessed to the Russell murders, according to the legal team working for Michael Stone, who has spent nearly two decades in jail for the killings.

Stone is serving two life sentences after being convicted of the murders of Lin Russell and her six-year-old daughter Megan, as well as the attempted murder of her nine-year-old daughter Josie, near the village of Chillenden, Kent in 1996.

But the claim that Bellfield has made a “very detailed confession” to a fellow prisoner that was corroborated by forensic evidence and witness testimony has raised the prospect Stone could be freed, his lawyers and sister Barbara said on Wednesday.

“We have now received evidence of a full confession by Levi Bellfield to the Russell murders,” Stone’s solicitor Paul Bacon told reporters. “In the confession, Bellfield describes how he came across Lin Russell and her two children, how he attacked them with a hammer, and his motivation for the killing. The confession is detailed and has a number of facts which are not in the public domain.”

Stone’s legal team said it had been made over the course of a few weeks and included “diagrams of where the murder took place and where the bodies were in situ”, as well as contemporaneous notes.

Besides that, they said, a witness had come forward to say she saw Bellfield near the scene of the crime at about the time it was committed. The woman gave her evidence to the police soon after the murders, but nothing came of it, Bacon said.

The lawyers acting for Stone also claimed to have forensic evidence that corroborated the claimed confession, though they declined to say what it was for fear of prejudicing any future proceedings. The new evidence has been handed to the Criminal Cases Review Commission, said Stone’s barrister Mark McDonald, as the legal team called for it to be tested by the court of appeal.

Barbara Stone said the new evidence was the “biggest hope that my brother’s had for a long time”.

She told reporters: “I understand there’s going to be some interest in the fact that it’s a confession of sorts, given that my brother was convicted by a confession. But ... the confession that convicted my brother, all that information was in the public domain. This information is different.”

She said she would never stop campaigning until her brother was freed. “I’d like to think that this will go to the court of appeal, they’ll hear the evidence, see that it would’ve made a difference at the original trial and that Mick will be released. And then maybe we’ll hit our retirement years and we’ll be able to live in peace.”

Stone has always maintained his innocence and has fought a protracted legal battle to clear his name over the hammer attack on the Russells. He was originally convicted of the crimes in 1998, but that was quashed by the court of appeal. He was convicted for a second time in 2001 and jailed.

On Wednesday, Stone’s solicitor stressed that, in contrast to Bellfield’s alleged confession, the “only evidence” against his client was a “confession said to have been heard by a notorious criminal”, Damien Daley, who had since admitted to lying to the jury during his evidence and was subsequently jailed for murder himself.

It is not the first time Stone’s legal representatives have pointed the finger at Bellfield. In 2011, Bacon claimed Bellfield was a better match for an efit of the suspect issued during the police manhunt.

In November last year, the Metropolitan police closed an investigation into serious crimes allegedly involving Bellfield, saying all lines of inquiry had been exhausted and officers had found no evidence linking him to any cases for which he had not already been convicted.

This week, Stone’s legal team said they expected Bellfield to deny having made the confession. They called him manipulative and stressed in their allegation that he had divulged information not in the public domain and that his account was corroborated by the other evidence.

They said the confession came from conversations between Bellfield and another prisoner that started because the serial killer was worried about how he would be portrayed in a recent documentary about the murders.

Bellfield, who now calls himself Yusuf Rahim, is serving two whole-life terms after being convicted of the murders of Amelie Delagrange, 22, Marsha McDonnell, 19, and Milly Dowler, 13, and of the attempted murder of Kate Sheedy, 18.

He was found guilty in 2008 of the murders of Delagrange in 2004 and McDonnell in 2003 and the attempted murder of Sheedy also in 2004. In 2011, while already in jail, he was convicted of abducting and killing Milly, who was snatched from the street on her way home from school in Walton-on-Thames, Surrey, in March 2002.

Stone’s legal team said they did not trust Kent police to be involved in investigating the new evidence and asked for it to be carried out by another force.

The Criminal Cases Review Commission, which dismissed an appeal in 2010, confirmed it received an application from Stone’s lawyers in August and the case was under investigation.